Edit: i know what modes are and how they are related to major scale..etc. question is about modal harmony and chord progression in modal harmony. not what is a mode and name of other modes..etc

What does that mean when we say a given song is in for instance in A Dorian mode?(like Beatles Eleanor Rigby)

First I thought simply we take the A Dorian scale then find the chord progression by taking every 1 3 5 interval of each note in that scale and end up with a series of chords to use in that KEY.

But later I learned that "dorian" mode is the opposite of a progression. Dorian is a "mode" (the second mode of the major scale) and implies a static harmony.

What does this static harmony mean? When I want to make a song on a specific mode, then how can I determine the usable chords or chord progression in that song? One thing I heard was I need to use unrelated chords so they don't pull your ear to a center. But how to determine in theory what is the "best" "unrelated" chords

I'm not entirely sure what you're looking for here, but Dorian doesn't imply a static harmony. A mode or a key is defining the primary notes that are used to make both melodies and harmonies, but the harmonies can be as dynamic or as static as you want. Writing in A Dorian means that you'll generally be using A, B, C, D, E, F#, and G and that A will generally be your home or goal note, but it doesn't necessarily say anything about the harmonies you will or won't use except for their specific note content.
– Pat MuchmoreMar 13 '14 at 17:34

2 Answers
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As far as I'm aware, Beatles' Eleanor Rigby is written in E Aeolian/minor (with the key signature of a G major/E minor, which is just one sharp at the F).

Although most of the song is mostly played in Aeolian, the verses are alternating with the Dorian mode. The Dorian mode is almost exactly the same as an Aeolian mode, but with a raised sixth! In this case the C becomes a C#.

A mode is just a scale, but are most commonly refered to in the context of "The seven modes" which are: Ionian, Dorian, Phrygian, Lydian, Mixo-Lydian, Aeolian and Locrian. These scales are all "modes" of each other, meaning that a C Ionian scale contains the same notes as a E Phrygian and a G Mixo-Lydian.

This song, however, is first played in E Aeolian, and then E Dorian.

That'll be the conclusion of this rough song analysis, now to your question about static harmony (versus dynamic harmony). These terms are fairly new to me, as I'm more familiar with classic functional analysis, and this is more of a modern approach (at least as far as I'm aware), but I'll do me best to explain them:

A static harmony is a term you're concerned with, when you're analyzing a a songs "syntactic structure". It is a harmony made from roughly one chord (most often the tonic of the dominant), and the prolongation of this chord.

A dynamic harmony, on the other hand, is made up from chord progressions - changing in chords. The most common of these harmonies being the authentic cadence (D-T) and the plagal cadence.

I find it important to note that a mode is not JUST a scale, in the same way that being in a given key is not just a major or minor scale. You can describe a mode as a scale but to say that you are in a given mode means that your tonal center is based there and primarily uses the notes of that scale. Some modal music is harmonically static, while some is dynamic. For instance, a very large amount of rock music is modal and definitely contains chord changes (like every Nirvana song).
– BassticklerMar 13 '14 at 18:15

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Also, this does not seem to answer the "how can I determine the usable chords or chord progression in that song?" part of the question. There are relatively standard chord progressions for each mode, similar to Dominant to Tonic, functional harmony. Some modes lend themselves a little more to a stable sounding harmonic progression, while others, such as Locrian and Phrygian, don't tend to be used as frequently, as they are less harmonically stable. Perhaps another question specifically geared toward modal chord progressions could be in order. Or maybe I should just write up an answer?
– BassticklerMar 13 '14 at 18:25

To my knowledge, there is no magic set of rules that will make your music sound "right." Instead, study the works of composers who frequently used the methods you want to learn. In this case: Palestrina, Josquin, William Byrd, et al. Also (surprise!) Bartok, Stravinsky, Copland ... For a treatise written when modes were at still in wide use, at least in Western music, try Gradus ad Parnassum by Johan Joseph Fux. Fux mostly discusses counterpoint, however, counterpoint easily abstracts to harmony and in many cases generates harmony; i.e., individual voice parts of follow the rules of counterpoint. Note that I have not mentioned any specific modes: chord movement and voice leading are more general concerns. It would be silly to repeat the information nicely explained by Bassticker.